Photonic irradiation induces nano-structures an EPR study

Size: px
Start display at page:

Download "Photonic irradiation induces nano-structures an EPR study"

Transcription

1 JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 9, No. 8, August 2007, p Photonic irrdition induces nno-structures n EPR study C. FLOREA *, S. GEORGESCU b ESIEE (Ecole Supérieure d'ingénieurs en Electronique et Electrotechnique de Pris) B.P. 99 F93162 NOISY-LE-GRAND cedex Frnce b NILPRP (Ntionl Institute for Lsers, Plsm, nd Rdition Physics) 409 Atomistilor Street / P.O. Box MG-54 RO Romni During the irrdition of fluorite (CF 2) with photons (X) we observe the formtion of nno ordered structures (inclusions). This forming structure is homothetic in reltion to the fluorine ions of the crystl. The prticles of pproximtely 10 nm size gglomerte nd form nnostructures structures with prllelipipedic shpe. The length of these structures vries between 30 nd 3000 nm. The locl chnges of symmetry produced by the formtion of the nno structures cn be inferred from EPR mesurements on Krmers rre erth ions introduced in CF 2. (Received Mrch 15, 2007; ccepted July 10, 2007) Keywords: Nnostructures structures with prllelipipedic shpe, Krmers rre erth ions, F centers, Locl symmetry chnge, Exciton, G ) tensor, Trigonl xes, Tetrgonl spectrum 1. Introduction A very lrge number of ppers were devoted to the study of the chnges induced in the irrdited crystls. Among the most significnt, in our opinion, re the ppers [1-4]. In these ppers it is evidenced the role of the point defects (essentilly, F centers) in the chnges ppering s the result of the irrdition with high-energy X photons (more thn 1 kev). It seems tht the F centers re produced ccording to the following scenrio [5,6]: the incident photons ionize minly the nionic sites. The nion ioniztion produces t the site positive chrge ( hole or n nionic vcncy). The vcncy trps n electron, which compenstes its positive chrge. The electron nd the vcncy constitute hydrogen-type object with chrcteristic energy levels. The resulting selective bsorption is responsible for the color of the crystl (normlly trnsprent). The ssembly nionic vcncy + electron is nmed F center (from the Germn word "Frbe" for color). To simplify, the F center cn be considered s cubic box contining n electron. The eigenvlues of the electronic energy re (if the potentil vnishes inside the h π 2 box nd is infinite outside): ( n ) 2 x + n y + nz, 2m0 where h is the rtionlized Plnck constnt, m 0 is the electron mss nd n x, n y, nz re non-null integer numbers. In the ground stte n x = n y = nz = 1, i. e. the ground stte is not degenerted. The first excited stte is three times degenerted: (2,1,1), (1,2,1), (1,1,2). The irrdition with photons could distort the site, nd tht is equivlent with locl symmetry chnge. This distortion reduces the symmetry of the F center, removing prtilly the degenercy, nd diminishes the energy of the defect. The energy-configurtion digrm [5] shows tht the stte (1,1,2) representing n elongtion or contrction of the lttice round the F center is predisposed to such distortion. This spontneous distortion of the F center (observed, lso, for other defects or crystls) is of the Jhn-Teller type. Due to this effect the energy of the stte is lowered, the energy being shred with two nionic neighbors, resulting n X 2 (Fluorine, in this cse) molecule oriented long <110> direction. This molecule, very electrophile, trps n electron which forms with the hole nother hydrogen-like stte, nmed exciton. This stte is shred by two neighboring nions. The locl distortion (for instnce, contrction) stbilizes this excited stte denoted (1,1,2). The rditive energy of the de-excittion, diminished by the lttice distortion, could tke the vlue zero (if the configurtiondistortion curves intersect ech other). In this cse the energy of this non-rditive trnsition is completely trnsferred to ions. Tking into ccount the symmetry, the most probble event is the ejection of one of the two ions A in the direction of the molecule X 2. This direction is dense nd formed by A ions of the sme mss. At the time of non-rditive de-excittion, n nion returns to its site while the other one, leving the site, send off the nerest neighbor. The origin of this process is the photon impct; successive impcts propgte with low losses. For enough initil energy (5-8 ev), the initil ion drives off its neighbor, this one drives off its neighbor nd so on. Finlly,

2 2304 fter this series of collisions, vcncy A remins in the initil position while n interstitil is present t some tomic distnces where two nions shre the sme site. The energy of the non-rditive trnsition cn be either found s the energy to crete the two defects (vcncy v nd the interstitil i ) or dissipted by the therml gittion during collisions. As conclusion, we must emphsize tht the cretion mechnism of the nno-structures by irrdition is not yet elucidted. In order to understnd better this mechnism, series of EPR experiments on irrdited smples doped with Krmers rre erth ions (Er 3+ nd Sm 3+ ), hs been crried out. 2. Experimentl C. Flore, S. Georgescu presence of n intense EPR signl chrcterized by G ) tensor with trigonl symmetry. This signl is very intense in the irrdited smple but it is present, with lower intensity, in non-irrdited smple EPR mesurements on irrdited smple The non-doped fluorine smple does not give ny EPR signl. After the irrdition with 50 kev X photons (4 hours nd, respectively, 8 hours) the EPR signls with g 2 re clerly observed. These EPR signls (Figs. 1 nd 2) were recorded for fixed frequency (9.4 GHz) nd vrible mgnetic field ( Guss). The CF 2 single crystls, doped with Er 3+ nd Sm 3+ hve been grown in the Solid Stte Quntum Electronics Lbortory - Ntionl Institute for Lsers, Plsm, nd Rdition Physics. Er 3+ nd Sm 3+ substitute C 2+ in the CF 2 lttice. Smrium enters, lso, s Sm 2+, with nonvnishing Vn Vleck susceptibility (χvv). This susceptibility influences the positions nd the intensities of the EPR signl of Sm 3+. Erbium enters only s Er 3+. The CF 2 single crystls were grown in rgon tmosphere. Prior to the growth, the CF 2 ws purified by therml tretments nd zone melting. The doping concentrtions were 1.5 % mol for Sm nd 0.1 % mol for Er. Smrium ws introduced s metl while Erbium ws introduced s Er 2 O 3. The initil concentrtions (in the nonirrdited smples) of Sm 3+ nd Er 3+ were the sme (0.05 t. % reltive to C 2+ ). Therefore, the intensity of Sm 3+ EPR signl hd the sme order of mgnitude s the Er 3+ signl. For crystlline structures of the fluorite type the EPR studies evidenced the role of the symmetry of the lignd field in the process of the energy trnsfer between the electronic energy levels. By irrditing such crystlline structure with X-rys (~50 kev) we observe tht the symmetry chnge of the lignd field induces the nisotropy of the G ) tensor (tensor of spectrl decomposition). In crystlline structure of fluorine type when the RE 3+ (RE = rre erth) ion enters site with cubic symmetry substituting divlent metl ion Me 2+, the EPR spectr of RE 3+ re rther complex. For Sm 3+ it is difficult to interpret the EPR spectr in the frme of the first order of perturbtion due to the smll gp (~1000 cm -1 ) between the first excited stte nd the ground stte 6 H 5/2. In contrst, the components g nd g of the G ) tensor re well identified. In this cse the gp between the first excited stte 4 I 3/2 nd the ground stte 4 I 15/2 is lrge enough (~6000 cm -1 ) nd thus the first order theory of perturbtions is correct. Due to the chrge compenstion, the site symmetry, initilly cubic, chnges into longitudinl tetrgonl nd/or into digonl trigonl symmetry. Nevertheless, some sites remin cubic. The new result reported in this pper is the b Fig. 1. The EPR signl recorded on CF 2 smple irrdited for 4 hours with 50 KeV X-ry photons. b The Poincré s fit evidences the complex structure of the line: - dominnt Lorentzin contribution (~85%) due to the F centers (thick, solid line); - minor Gussin contribution (~15%) due to the conduction electrons (thin, dotted line).

3 Photonic irrdition induces nno-structures n EPR study Smrium-doped smple In CF 2 the smrium ion (divlent or trivlent) substitutes the divlent ction C 2+. Sm 2+ is not prmgnetic but posses Vn Vleck susceptibility. This susceptibility could produce, in certin neighborhood conditions, shift of the EPR signl of Sm 3+ centers Experiments on non-irrdited smples The EPR spectr were recorded t 4 K for fixed frequency (9.46 GHz) with mgnetic field vrying between 7000 nd Guss. Our mesurements show the presence of centers corresponding to two types of symmetry: ones with cubic nd others with lower symmetry (C 4v ). In the lst cse the G ) tensor corresponds to the xil symmetry of the xes [100], [010] or [001]. We obtined g = 0.90±0.01 nd g = 0.77±0.01. The verge vlue is g ~ long the direction <100>. This vlue is higher thn vlue for the isotropic g, corresponding to the cubic symmetry for Γ 7 (g 0.467). This proves the existence of mgnetic exchnge between Sm 3+ nd Sm 2+. The exchnge provokes, lso, Δg shift. The Sm 3+ spectrum contins, for n rbitrry ngle, three lines (Fig. 3). b Fig. 2. The EPR signl recorded on CF 2 smple irrdited for 8 hours with 50 KeV X-ry photons. b The reltive contributions of Lorentzin (F centers - thick, solid line) nd of Gussin (conduction electrons - thin, dotted line) lines chnges from 85 % : 15 % to 55 % : 45 %. Using the Poincré fit method [8] we put in evidence the complexity of the EPR signl: Lorentzin line (due to F centers) nd Gussin line (due to the conduction electrons) re superimposed. The mesurements evidenced the increse of signl of the conduction electrons s one goes long the formtion of the metl nno-structures in the crystlline structure of CF 2. The CF 2 structure is initilly insulting nd without ny mgnetiztion. Once irrdited, the presence of EPR signl typicl for F centers [1] supports our hypothesis concerning the role plyed by this type of defects in the formtion of the nnometer metl inclusions. The experiments on doped smples llowed to refine our models. Fig. 3. EPR signl of Sm 3+ : CF 2 irrdited 8 hours with 50 kev X photons. For vrious orienttions the vlues of g show n ngulr nisotropy. For n xil symmetry of the crystl field type <100> there re, for n ngle θ, three clsses of resontors, ccording to the three possibilities: [100], [010] nd [001]. If θ is the ngle between [100] direction nd the mgnetic field H r 0, the ngle θ tkes the vlues π π θ, θ nd for the resontors x, y, z.

4 2306 C. Flore, S. Georgescu Experiments on irrdited smples The irrdition with 50 kev X-rys leds to the formtion of point defects. These defects fvor supplementry vlence chnge Sm 2+ Sm 3+. This chnge is produced by n extrinsic mechnism due to interstitil de-loction of Sm or by the vicinity of defect in the lignd lttice. The lst possibility seems to be more probble, the formtion of fluorine vcncies being the most probble process t this irrdition level. As result of the irrdition, globl increses of ~ 10% of the EPR signl due to the increse of the number of resonnt centers. On the other hnd, the line positions re shifted, s result of the new numericl presence of the Sm 2+ ions. The lst effect is provoked by the modifiction (vi the number p of the Sm 2+ nerest neighbors) of the Vn Vleck susceptibility. This suggests tht pproximtely 10% Sm 2+ ions becme Sm 3+. [010] nd [001] crystl xes. The proposed nottions for [100], [010] nd [001] crystl xes re: T X, T Y nd T Z. The four trigonl xes correspond to the directions, 111, [ 111 ] [ ] [ ] nd [ ] Experiments on non-irrdited smples The EPR spectr were recorded t 4 K nd 9.46 GHz. The mgnetic field vries round 1000 Guss. The digrm [ g / sin θ] gives the components of the G ) tensor. The results re given in Tble 1. Tble 1. Components of the G ) tensor in non-irrdited Er 3+ : CF 2. Components of the G ) g tensor g Symmetry Cubic Tetrgonl Trigonl The obtined vlues re close to the vlues reported by Rnon nd Low [7] for the tetrgonl spectrum of the type I, i. e. g = 7.78 nd g = 8.54 (Fig. 5), but we found very different intensities, corresponding to the sme ngulr vlues of the mgnetic field reltive to the T Z xis. For the non-irrdited smple we found tht the Fig. 4. Digrm [ θ] 2 ; sin 2 g for Sm 3+ : CF 2 irrdited 8 hours with 50 kev X photons. In this cse, the chrge compenstion plys determinnt role when the symmetry of the lignd field chnges. The nlysis of the EPR signls of Sm 3+, modified by the symmetry chnge of the sites, is very difficult tsk. As we lredy mentioned, the gp between the ground ste 6 H 5/2 nd the first excited stte 6 H 7/2 is rther smll (~1000 cm -1 ). It is esier to interpret these symmetry chnges for the EPR signls of Er 3+ ions: the energy gp seprting the ground stte 4 I 15/2 nd the first excited stte 4 I 13/2 is much lrger (~6000 cm -1 ) Erbium-doped smple The trivlent Er 3+ ions enter the cubic structure of CF 2 by heterovlent substitution of C 2+. The chrge compenstion induces the formtion of defect which modifies the site symmetry. Three types of symmetry re evidenced: cubic, tetrgonl nd / or trigonl. In tetrgonl symmetry there re three equivlent sites long the [100], Fig. 5. Angulr dependence of the components of the G ) tensor in non-irrdited Er 3+ : CF 2 ; θ is the ngle between [100] direction nd the mgnetic field H r 0. intensities of the signls re in the following rtios: T (tetrgonl) : t (trigonl) : c (cubic) = 4 : 2 : 3. No tetrgonl or trigonl signl of the type II (cited in [7]) ws detected in our spectr.

5 Photonic irrdition induces nno-structures n EPR study Experiments on irrdited smples For the irrdited smples the lines hve the ngulr evolution given I Fig. 6. The ngulr digrms were constructed from the EPR spectr whose prmeters were identified using the Poincré s tretment [8]. 3. Conclusion The comprison of Er 3+ EPR spectr in irrdited nd in non-irrdited CF 2 smples led us to the following conclusions: - the lines conserve their ngulr dependence; - the intensity of the cubic lines decreses; - the intensity of the tetrgonl lines increses slightly; - the intensity of the trigonl lines shows significnt increse; - the totl number of resonnt Er 3+ centers is rigorously the sme in both irrdited nd non-irrdited smples. We put in evidence symmetry chnge of the lignds F from cubic towrd C 4V. The tetrgonl chnge is explined s result of chrge compenstion with n interstitil defect creted by n F- ion occupying the center of the neighbor lignds, initilly empty. In the trigonl cse we suggest tht n O 2- ion replces F ion in cube corner of neighboring fluorine ions. Fig. 6. Angulr dependence of the components of the G ) tensor in Er 3+ : CF 2 irrdited 8 hours with 50 kev X photons. In this cse, the intensity rtio is T : t : c = 8 : 5 : 4. We must emphsize tht our crystls were grown in neutrl tmosphere. The significnt increses of the trigonl signl in the irrdited smples re probbly due to the presence of oxygen. We suppose tht the bsence of the trigonl spectr of type II (whose intensity increse is reported in [7]) is relted to compenstion with oxygen plced digonlly in fluorine position. This oxygen cme from the Er 2 O 3 doping. References [1] F. Beuneu, C. Flore, P. Vjd Rdition Effects nd Defects in Solids, 136, 175, (1995). [2] Ch. T. de Montpreville Note Technique SRPM CEA (1985). [3] E. Johnson, L. Chderton Rdition Effects nd Defects in Solids, 79, 183 (1983). [4] A. Hughes, S. Jin Adv. in Phys., 28, 717 (1979). [5] Y. Quéré Points Deffects in Solids, Msson Ed. Pris (1967). [6] Ch. H. de Novion Note Technique SESI CEA (1993). [7] U. Rnon, W. Low Phys. Rev , (1963). [8] C. Flore Note Technique SESI CEA (1994). * Corresponding uthor: c.flore@esiee.fr

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING

More information

Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions

Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions Quntum Mechnics Qulifying Exm - August 016 Notes nd Instructions There re 6 problems. Attempt them ll s prtil credit will be given. Write on only one side of the pper for your solutions. Write your lis

More information

Analogy Between Particle in a Box and Jahn Teller Effect

Analogy Between Particle in a Box and Jahn Teller Effect Anlogy Between Prticle in Box nd Jhn Teller Effect MNMurty MNMurtyis Professor in Physics t Ntionl Institute of Science nd Technology, Plur Hills, Berhmpur, Odish. The energy levels of prticle in box re

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

Period #2 Notes: Electronic Structure of Atoms

Period #2 Notes: Electronic Structure of Atoms Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find seven questions covering vries topics rnging from the structure of molecules, ions, nd solids to different models for explining bonding. Red

More information

5.04 Principles of Inorganic Chemistry II

5.04 Principles of Inorganic Chemistry II MIT OpenCourseWre http://ocw.mit.edu 5.04 Principles of Inorgnic Chemistry II Fll 2008 For informtion bout citing these mterils or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.04, Principles of

More information

Lecture 8. Band theory con.nued

Lecture 8. Band theory con.nued Lecture 8 Bnd theory con.nued Recp: Solved Schrodinger qu.on for free electrons, for electrons bound in poten.l box, nd bound by proton. Discrete energy levels rouse. The Schrodinger qu.on pplied to periodic

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn (2014) SOLID STATE PHYSICS 2 HOURS The pper is divided into 5 questions. Answer

More information

Prof. Anchordoqui. Problems set # 4 Physics 169 March 3, 2015

Prof. Anchordoqui. Problems set # 4 Physics 169 March 3, 2015 Prof. Anchordoui Problems set # 4 Physics 169 Mrch 3, 15 1. (i) Eight eul chrges re locted t corners of cube of side s, s shown in Fig. 1. Find electric potentil t one corner, tking zero potentil to be

More information

Crystalline Structures The Basics

Crystalline Structures The Basics Crystlline Structures The sics Crystl structure of mteril is wy in which toms, ions, molecules re sptilly rrnged in 3-D spce. Crystl structure = lttice (unit cell geometry) + bsis (tom, ion, or molecule

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn (015) SOLID STATE PHYSICS HOURS The pper is divided into 5 questions. Answer compulsory

More information

- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.

- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students. - 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting

More information

Vibrational Relaxation of HF (v=3) + CO

Vibrational Relaxation of HF (v=3) + CO Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,

More information

Name Solutions to Test 3 November 8, 2017

Name Solutions to Test 3 November 8, 2017 Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS

Data Provided: A formula sheet and table of physical constants is attached to this paper. SOLID STATE PHYSICS Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn (2016) SOLID STATE PHYSICS 2 HOURS Instructions: The pper is divided into 5 questions.

More information

Energy creation in a moving solenoid? Abstract

Energy creation in a moving solenoid? Abstract Energy cretion in moving solenoid? Nelson R. F. Brg nd Rnieri V. Nery Instituto de Físic, Universidde Federl do Rio de Jneiro, Cix Postl 68528, RJ 21941-972 Brzil Abstrct The electromgnetic energy U em

More information

2.57/2.570 Midterm Exam No. 1 March 31, :00 am -12:30 pm

2.57/2.570 Midterm Exam No. 1 March 31, :00 am -12:30 pm 2.57/2.570 Midterm Exm No. 1 Mrch 31, 2010 11:00 m -12:30 pm Instructions: (1) 2.57 students: try ll problems (2) 2.570 students: Problem 1 plus one of two long problems. You cn lso do both long problems,

More information

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere

More information

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

PHY 140A: Solid State Physics. Solution to Midterm #1

PHY 140A: Solid State Physics. Solution to Midterm #1 PHY 140A: Solid Stte Physics Solution to Midterm #1 TA: Xun Ji 1 October 24, 2006 1 Emil: jixun@physics.ucl.edu Problem #1 (20pt)Clculte the pcking frction of the body-centered cubic lttice. Solution:

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

Phys 7221, Fall 2006: Homework # 6

Phys 7221, Fall 2006: Homework # 6 Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 3-7 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which

More information

Appendix A Light Absorption, Dispersion and Polarization

Appendix A Light Absorption, Dispersion and Polarization 73 Aendix A Light Absortion, Disersion nd Polriztion A. Electromgnetic Sectrum The electromgnetic sectrum (Figure A.) is divided into seven min domins rnged ccording to their wvelength λ. We hve λ ct c=ν

More information

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler) CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

8 Laplace s Method and Local Limit Theorems

8 Laplace s Method and Local Limit Theorems 8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved

More information

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The two-dimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero

More information

Key for Chem 130 Second Exam

Key for Chem 130 Second Exam Nme Key for Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding.

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk bout solving systems of liner equtions. These re problems tht give couple of equtions with couple of unknowns, like: 6 2 3 7 4

More information

QUB XRD Course. The crystalline state. The Crystalline State

QUB XRD Course. The crystalline state. The Crystalline State QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by

More information

Supplementary Figure 1 Supplementary Figure 2

Supplementary Figure 1 Supplementary Figure 2 Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully

More information

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah 1. Born-Oppenheimer pprox.- energy surfces 2. Men-field (Hrtree-Fock) theory- orbitls 3. Pros nd cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usully does HF-how? 6. Bsis sets nd nottions 7. MPn,

More information

Li ion diffusion mechanism in the crystalline electrolyte γ-li 3 PO 4

Li ion diffusion mechanism in the crystalline electrolyte γ-li 3 PO 4 Li ion diffusion mechnism in the crystlline electrolyte γ-li 3 Yojun Du nd N. A. W. Holzwrth The structure of thin film bttery 3 Solid stte electrolyte could be mde very thin to overcome to the low ionconductivity.

More information

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

Field-Induced Axion Luminosity of Photon Gas via a-interaction N.V. Mikheev, A.Ya. Parkhomenko and L.A. Vassilevskaya Yaroslavl State (Demidov) Univer

Field-Induced Axion Luminosity of Photon Gas via a-interaction N.V. Mikheev, A.Ya. Parkhomenko and L.A. Vassilevskaya Yaroslavl State (Demidov) Univer Field-Induced Axion Luminosity of Photon Gs vi -Interction N.V. Mikheev, A.Y. Prkhomenko nd L.A. Vssilevsky Yroslvl Stte (Demidov) University, Sovietsky 14, Yroslvl 150000, Russi Abstrct The interction

More information

Classical Mechanics. From Molecular to Con/nuum Physics I WS 11/12 Emiliano Ippoli/ October, 2011

Classical Mechanics. From Molecular to Con/nuum Physics I WS 11/12 Emiliano Ippoli/ October, 2011 Clssicl Mechnics From Moleculr to Con/nuum Physics I WS 11/12 Emilino Ippoli/ October, 2011 Wednesdy, October 12, 2011 Review Mthemtics... Physics Bsic thermodynmics Temperture, idel gs, kinetic gs theory,

More information

Physics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:

Physics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions: Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You

More information

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

More information

December 4, U(x) = U 0 cos 4 πx 8

December 4, U(x) = U 0 cos 4 πx 8 PHZ66: Fll 013 Problem set # 5: Nerly-free-electron nd tight-binding models: Solutions due Wednesdy, 11/13 t the time of the clss Instructor: D L Mslov mslov@physufledu 39-0513 Rm 11 Office hours: TR 3

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

Session 13

Session 13 780.20 Session 3 (lst revised: Februry 25, 202) 3 3. 780.20 Session 3. Follow-ups to Session 2 Histogrms of Uniform Rndom Number Distributions. Here is typicl figure you might get when histogrmming uniform

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

Analytical Methods for Materials

Analytical Methods for Materials Anlyticl Methods for Mterils Lesson 7 Crystl Geometry nd Crystllogrphy, Prt 1 Suggested Reding Chpters 2 nd 6 in Wsed et l. 169 Slt crystls N Cl http://helthfreedoms.org/2009/05/24/tble-slt-vs-unrefined-se-slt--primer/

More information

13.4 Work done by Constant Forces

13.4 Work done by Constant Forces 13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push

More information

P812 Midterm Examination February Solutions

P812 Midterm Examination February Solutions P8 Midterm Exmintion Februry s. A one dimensionl chin of chrges consist of e nd e lterntively plced with neighbouring distnce. Show tht the potentil energy of ech chrge is given by U = ln. 4πε Explin qulittively

More information

1.Bravais Lattices The Bravais lattices Bravais Lattice detail

1.Bravais Lattices The Bravais lattices Bravais Lattice detail 1.Brvis Lttices 12.1. The Brvis lttices 2.2.4 Brvis Lttice detil The Brvis lttice re the distinct lttice types which when repeted cn fill the whole spce. The lttice cn therefore be generted by three unit

More information

Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

How to simulate Turing machines by invertible one-dimensional cellular automata

How to simulate Turing machines by invertible one-dimensional cellular automata How to simulte Turing mchines by invertible one-dimensionl cellulr utomt Jen-Christophe Dubcq Déprtement de Mthémtiques et d Informtique, École Normle Supérieure de Lyon, 46, llée d Itlie, 69364 Lyon Cedex

More information

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles Method of Loclistion nd Controlled Ejection of Swrms of Likely Chrged Prticles I. N. Tukev July 3, 17 Astrct This work considers Coulom forces cting on chrged point prticle locted etween the two coxil,

More information

Quantum Physics I (8.04) Spring 2016 Assignment 8

Quantum Physics I (8.04) Spring 2016 Assignment 8 Quntum Physics I (8.04) Spring 206 Assignment 8 MIT Physics Deprtment Due Fridy, April 22, 206 April 3, 206 2:00 noon Problem Set 8 Reding: Griffiths, pges 73-76, 8-82 (on scttering sttes). Ohnin, Chpter

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,

More information

Entanglement of an Atom and Its Spontaneous Emission Fields via Spontaneously Generated Coherence

Entanglement of an Atom and Its Spontaneous Emission Fields via Spontaneously Generated Coherence Journl of Sciences Islmic Republic of Irn (): 7-76 () University of Tehrn ISSN 6-4 http://jsciences.ut.c.ir Entnglement of n Atom nd Its Spontneous Emission Fields vi Spontneously Generted Coherence M.

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

1 Bending of a beam with a rectangular section

1 Bending of a beam with a rectangular section 1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure

More information

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials:

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials: Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=

More information

Chapter 16 Acid Base Equilibria

Chapter 16 Acid Base Equilibria Chpter 16 Acid Bse Equilibri 16.1 Acids & Bses: A Brief Review Arrhenius cids nd bses: cid: n H + donor HA(q) H(q) A(q) bse: n OH donor OH(q) (q) OH(q) Brønsted Lowry cids nd bses: cid: n H + donor HA(q)

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Experiment S-10: Optical Pumping. Physics 510

Experiment S-10: Optical Pumping. Physics 510 Experiment S-10: Opticl Pumping Physics 510 Drren Puigh Dted: Februry 27, 2006) This experiment used the process of opticl pumping to investigte the hyperfine splitting of two rubidium isotopes in the

More information

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL V. Bkhnov, O. Kryvook, B. Dormn Ukrinin Hydrometeorologicl Reserch Institute, Avenue of Science 37,

More information

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004 Advnced Clculus: MATH 410 Notes on Integrls nd Integrbility Professor Dvid Levermore 17 October 2004 1. Definite Integrls In this section we revisit the definite integrl tht you were introduced to when

More information

Heat flux and total heat

Heat flux and total heat Het flux nd totl het John McCun Mrch 14, 2017 1 Introduction Yesterdy (if I remember correctly) Ms. Prsd sked me question bout the condition of insulted boundry for the 1D het eqution, nd (bsed on glnce

More information

ragsdale (zdr82) HW2 ditmire (58335) 1

ragsdale (zdr82) HW2 ditmire (58335) 1 rgsdle (zdr82) HW2 ditmire (58335) This print-out should hve 22 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 00 0.0 points A chrge of 8. µc

More information

Physics 2135 Exam 1 February 14, 2017

Physics 2135 Exam 1 February 14, 2017 Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted

More information

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011 Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you

More information

UNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences UNIVERSITY OF OSLO Fculty of Mthemtics nd Nturl Sciences Midterm exm in MENA3100 Dy of exm: 19 th Mrch 2018 Exm hours: 14:30 17:30 This exmintion pper consists of 4 pges including 1 ppendix pge. Permitted

More information

Some parameters of varicaps with gradient base area based on Shottky barrier

Some parameters of varicaps with gradient base area based on Shottky barrier ISSN: 35-38 Vol. 4, Issue, December 7 Some prmeters of vricps with grdient bse re bsed on Shottky brrier Mmtkrimov O.O., KuchkrovB.Kh. Rector, Nmngn engineering-technology institute, Kosonsoy str.,7, Nmngn,

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI:.38/NMAT343 Hybrid Elstic olids Yun Li, Ying Wu, Ping heng, Zho-Qing Zhng* Deprtment of Physics, Hong Kong University of cience nd Technology Cler Wter By, Kowloon, Hong Kong, Chin E-mil: phzzhng@ust.hk

More information

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.

More information

The solutions of the single electron Hamiltonian were shown to be Bloch wave of the form: ( ) ( ) ikr

The solutions of the single electron Hamiltonian were shown to be Bloch wave of the form: ( ) ( ) ikr Lecture #1 Progrm 1. Bloch solutions. Reciprocl spce 3. Alternte derivtion of Bloch s theorem 4. Trnsforming the serch for egenfunctions nd eigenvlues from solving PDE to finding the e-vectors nd e-vlues

More information

Recitation 3: More Applications of the Derivative

Recitation 3: More Applications of the Derivative Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech

More information

Physics 24 Exam 1 February 18, 2014

Physics 24 Exam 1 February 18, 2014 Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Tody s Topics Sources of the Mgnetic Field (Ch. 28) Biot-Svrt Lw Ampere s Lw Mgnetism in Mtter Mxwell s Equtions Homework #7: due Tues 3/11 t 11 PM (4th problem optionl) Mgnetic

More information

Sufficient condition on noise correlations for scalable quantum computing

Sufficient condition on noise correlations for scalable quantum computing Sufficient condition on noise correltions for sclble quntum computing John Presill, 2 Februry 202 Is quntum computing sclble? The ccurcy threshold theorem for quntum computtion estblishes tht sclbility

More information

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics Solid Stte Physics JEST-0 Q. bem of X-rys is incident on BCC crystl. If the difference between the incident nd scttered wvevectors is K nxˆkyˆlzˆ where xˆ, yˆ, zˆ re the unit vectors of the ssocited cubic

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding. Red ech

More information

Phys 6321 Final Exam - Solutions May 3, 2013

Phys 6321 Final Exam - Solutions May 3, 2013 Phys 6321 Finl Exm - Solutions My 3, 2013 You my NOT use ny book or notes other thn tht supplied with this test. You will hve 3 hours to finish. DO YOUR OWN WORK. Express your nswers clerly nd concisely

More information

1 Online Learning and Regret Minimization

1 Online Learning and Regret Minimization 2.997 Decision-Mking in Lrge-Scle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in

More information

Module 6: LINEAR TRANSFORMATIONS

Module 6: LINEAR TRANSFORMATIONS Module 6: LINEAR TRANSFORMATIONS. Trnsformtions nd mtrices Trnsformtions re generliztions of functions. A vector x in some set S n is mpped into m nother vector y T( x). A trnsformtion is liner if, for

More information

Consequently, the temperature must be the same at each point in the cross section at x. Let:

Consequently, the temperature must be the same at each point in the cross section at x. Let: HW 2 Comments: L1-3. Derive the het eqution for n inhomogeneous rod where the therml coefficients used in the derivtion of the het eqution for homogeneous rod now become functions of position x in the

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

More information

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system Supplementry Mteril for Wve-pinning nd cell polrity from bistble rection-diffusion system Yoichiro Mori, Alendr Jilkine nd Leh Edelstein-Keshet Model Comprisons We concentrte here the three systems to

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. Linear-linear graph paper is required.

Data Provided: A formula sheet and table of physical constants is attached to this paper. Linear-linear graph paper is required. Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Liner-liner grph pper is required. DEPARTMENT OF PHYSICS AND ASTRONOMY Spring Semester (2015-2016) SEMICONDUCTOR PHYSICS

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. Linear-linear graph paper is required.

Data Provided: A formula sheet and table of physical constants is attached to this paper. Linear-linear graph paper is required. Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Liner-liner grph pper is required. DEPARTMENT OF PHYSICS AND ASTRONOMY Spring Semester (015) SEMICONDUCTOR PHYSICS AND TECHNOLOGY

More information

Sample Exam 5 - Skip Problems 1-3

Sample Exam 5 - Skip Problems 1-3 Smple Exm 5 - Skip Problems 1-3 Physics 121 Common Exm 2: Fll 2010 Nme (Print): 4 igit I: Section: Honors Code Pledge: As n NJIT student I, pledge to comply with the provisions of the NJIT Acdemic Honor

More information

Quantum Analogs Chapter 4 Student Manual

Quantum Analogs Chapter 4 Student Manual Quntum Anlogs Chpter 4 Student Mnul Modeling One Dimensionl Solid Professor Rene Mtzdorf Universitet Kssel Stud. Mn. Rev 2.0 12/09 4. Modeling one-dimensionl solid There re two different wys to explin

More information

Electron Correlation Methods

Electron Correlation Methods Electron Correltion Methods HF method: electron-electron interction is replced by n verge interction E HF c E 0 E HF E 0 exct ground stte energy E HF HF energy for given bsis set HF Ec 0 - represents mesure

More information

STRUCTURAL ISSUES IN SEMICONDUCTORS

STRUCTURAL ISSUES IN SEMICONDUCTORS Chpter 1 STRUCTURAL ISSUES IN SEMICONDUCTORS Most semiconductor devices re mde from crystlline mterils. The following gures provide n overview of importnt crystlline properties of semiconductors, like

More information

The Isotopic Shift in the Spectrum of Plutonium

The Isotopic Shift in the Spectrum of Plutonium SOVIET PHY.SICS- JETP V L U ME 1, N U M B E R. 2 SEPTEMBER, 1955 The Isotopic Shift in the Spectrum of Plutonium A. R. STRIGANOV, L. A. KoosTYLEV A AND lu. P. DoNTsov (Submitted to JETP editor July 27,

More information

Homework 4 , (1) 1+( NA +N D , (2)

Homework 4 , (1) 1+( NA +N D , (2) Homework 4. Problem. Find the resistivity ρ (in ohm-cm) for piece of Si doped with both cceptors (N A = 9 cm 3 ) nd donors (N D = 6 cm 3 ). Since the electron nd hole mobilities depend on the concentrtion

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory 2. Diffusion-Controlled Reaction

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory 2. Diffusion-Controlled Reaction Ch. 4 Moleculr Rection Dynmics 1. Collision Theory. Diffusion-Controlle Rection Lecture 17 3. The Mteril Blnce Eqution 4. Trnsition Stte Theory: The Eyring Eqution 5. Trnsition Stte Theory: Thermoynmic

More information

Problems for HW X. C. Gwinn. November 30, 2009

Problems for HW X. C. Gwinn. November 30, 2009 Problems for HW X C. Gwinn November 30, 2009 These problems will not be grded. 1 HWX Problem 1 Suppose thn n object is composed of liner dielectric mteril, with constnt reltive permittivity ɛ r. The object

More information

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite

More information